4.6. Exercises

1. Fully Connected Network. Given a grayvalue image \(f\) of size \(N\times N\) and a resulting image \(g\) of the same size, calculate the dimensions of the weight matrix \(W\) as used in the equation \(\v g = W \v f\) (see Eq. (4.4)).

2. Convolution/Correlation as Matrix-Vector Multiplication.

   1. In Eq. (4.5) the matrix corresponding with a correlation with a small kernel of a \(4\times4\) image is shown. Which border mode is implicitly used (either the constant value mode (what value?) or wrap mode)?

   2. What does the matrix \(W\) looks like for the other border mode?